Quenched penguins, the Delta I=1/2 rule, and epsilon'/epsilon

TL;DR

This paper investigates how quenched approximations in lattice QCD affect the analysis of non-leptonic kaon decays, revealing intrinsic ambiguities that impact the calculation of the Delta I=1/2 rule and epsilon'/epsilon, except in specific partially quenched scenarios.

Contribution

It provides a comprehensive analysis of the transformation properties of strong penguin operators in (partially) quenched QCD, highlighting the resulting ambiguities in lattice computations of kaon decay parameters.

Findings

Quenched approximations introduce intrinsic ambiguities in operator transformation properties.

These ambiguities affect lattice calculations of the Delta I=1/2 rule and epsilon'/epsilon.

Partially quenched case with three light sea quarks remains consistent with expectations.

Abstract

The transformation properties of strong penguin operators under the action of the flavor group change when they are considered as operators in (partially) quenched QCD instead of the unquenched theory. An ambiguity arises, which is parameterized by new low-energy constants in the effective theory describing non-leptonic kaon decays in the (partially) quenched setting. Here we summarize results of the analysis for the complete set of three-flavor strong penguin operators, consisting of products of two left-handed flavor currents, or a left- and a right-handed current. Our results imply that (partially) quenched lattice computations of the Delta I=1/2 rule and epsilon'/epsilon are both affected by ambiguities intrinsic to the use of the quenched approximation at leading order in the chiral expansion. The only exception is the partially quenched case with three light sea quarks, consistent with general expectations. We also address the issue of quenched ambiguities in the case of an active charm, correcting and extending that in Phys. Rev. D 74, 014509 (2006).